The Partial Model Matching Problem (or equivalently, the Partial Disturbance Rejection Problem) is revisited here. It has been initially introduced in [2] and amounts to matching the first kappa Markov parameters of the plant with those of the model. This obviously finds all its interest when no solution exists to the Exact Problem. We give both geometric and structural solutions to these problems. The geometric solution is in terms of the steps of the well known supremal output nulling controlled invariant subspace algorithm. The structural conditions amount to comparing some list of integers, namely some orders of zeros at infinity.